Formal Deformations of Dirac Structures

Details Formal Deformations of Dirac Structures Formal Deformations of Dirac Structures

2006-06-27

arxiv.org/abs/math/0606674v2

Mathematics

Quantum Algebra

LaTeX 2e, 26 pages, no figures. Minor changes and improvements

Scientific paper

10.1016/j.geomphys.2006.08.005

In this paper we set-up a general framework for a formal deformation theory of Dirac structures. We give a parameterization of formal deformations in terms of two-forms obeying a cubic equation. The notion of equivalence is discussed in detail. We show that the obstruction for the construction of deformations order by order lies in the third Lie algebroid cohomology of the Dirac structure. However, the classification of inequivalent first order deformations is not given by the second Lie algebroid cohomology but turns out to be more complicated.

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